(a) Find Vƒ where f(x, y) = log vx² + y².

Q: X* Q: Prove that the function y- 2 2 x+1+/log Vx+Jx +1 + log satisfies the relationship 2y=x dx

A:

Q: find the general solution for the displacement, x(t) mx''(t) + kx(t) = 0 t is time x is…

A: find the general solution for the displacement, x(t)

Q: Find F '(x). sin(x) F(x) = 3Vt dt

A:

Q: 17. The displacement (in meters) of a particle in motion is given by a= dt -t², where t is measured…

A: The displacement function is provided. And, we know that velocity is the derivative of time. So,…

Q: Use logarithmic differentiation to find the derivative, , of y = (t + 2)(t + 7)(t + 2). dt Choose…

A: The given function is y=(t+2)(t+7)(t+2). Take logarithm on both sides and simplify as follows.

Q: 2.) w'of w = (4v² – 7)2+v»²+5 using logarithmic differentiation

A: Using Logarithmic Differentiation.

Q: 1 dx = +C (x+1)² X+1

A:

Q: Find the antiderivative for each function when C equals 0. Check your answers by differentiation. 7…

A: Integrate. ∫hx=∫sec2xdxHx=tanx+C=tanx+0=tanx   Check by differentiating. ddxHx=ddxtanx=sec2x…

Q: Q2] can transmit the disease but who exhibit no overt symptoms. Let r and y denote the proportions o…

A: Here c1 is arbitary .

Q: Use Green's function to solve: y" – 4y' + 3y = ex, y(0) = 1, y'(0) = %3D

A: Introduction: Green's function is another method to solve an initial value problem. Green's function…

Q: 1) Find the second derivative of y = csc 2 e cot 2e %3D

A:

Q: to determine the approximate value of v(1+x³)dx

A:

Q: se C for the constant oT integration.) (7 cos x + 3 sin x) dx

A:

Q: What is the value of f (5) if f (t) sin (Ta) dt :? 1

A: Given, ∫1xfttdt = sinπxx   We have to find the value of f5

Q: Solve using separation of variables: dx = +(1 + t^2) sec^2 x dt.

A: Given differential equation, dx = ( 1+t2 )sec2x dt

Q: Q5:The derivative of: y(Y)= log,(sin (Y )cos (Y ))- log,(2*e

A:

Q: y are both differentiable functions of t. Equation Find Given 1. y = 3x - 5x when x = 3 32 at dy = 4…

A: Since you have asked multiple questions in single request.so we will be answering only first…

Q: Water is being drained from a spout in the bottom of a cylindrical tank. According to the…

A: Given  , Rate if drain: dV/dt = - 1.8L/min By integrating the equation we get the volume.

Q: One model for the spread of epidemics assumes that the number of people infected changes at a rate…

A: Here we will verified the given solution.

Q: where a = If loga z= dt, then r= exp

A:

Q: order differential coefficients as serie (b) y) when y = (7) sin 50. 50

A:

Q: Question 3 Using appropriate rules of integration, find S V1 + t² t5dt.

A: ∫xndx=xn+1n+1+C

Q: Find dx dy for y = Vx log, (x' – tan x). Do not simplify your ar

A:

Q: z(r) = cosʻ(r)/1+r² ?

A: given equation  apply natural log

Q: Q1: Using natural log., the derivative of : z(r) = cosʻ(r)/1+r² ?

A: The objective is to use natural logarithm to find the derivative of  z(r) .

Q: g(x) - (x)/ A.If f(x) = dt, where g(x) = + sin(tº )]dt, find f'(÷). (1

A:

Q: 1+vx dx use u= 1+ V 1- use Vx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let y = (r-15x)m(). Find dy using the method of logarithmic d.x differentiation. Express your answer…

A: We will solve the problem

Q: 4 196 x + 28 + 1 Let y= x> 0. - dy Find and simplify your answer Completely. 2 dx Hint : Before…

A: Topic - double derivative of a function

Q: dy using the method of logarithmic dx 4 tan a Find Let y = (In x)“ differentiation. Express your…

A: We can solve the given problem using concept of differentiate above equation with respect to x

Q: Integrate تلد ا - تم( فیگ S (a² – v²) * 22)* dv where " a" is constant

A:

Q: 9. Find the most general antiderivative; verify your answer by differentiation. a) f(x) = 2x*-Sx + 7…

A: a) on doing integration we get =2x^4/4-5x^2/2+7x+c this is the anti derivative of given function  on…

Q: Differentiate the function. y (x) = esin 2x + sin(e2")

A: It is given that, yx=esin  2x+sine2xWe have to differentiate the given function.

Q: Q4/ Use Logarithmic Differentiation to find dy/dx for the following functions: 1. y = V(x2 + 1)(x –…

A: Differentiation of ln(ax+b) = a/(ax+b)

Q: Find dy/dx by implicit differentiation. y tan(x – y) 7 + x2 y' = Need Help? Read It

A:

Q: Differentiate the function F(t) = (ln t)2 sin t

A: Given function is,

Q: x* +x?y² + y³ = 5

A: x4 + x2y2 + y3 = 5 Differentiating with respect to x; 4x3 + x2(2y* dy/dx) + y2(2x) + 3y2 (dy/dx) = 0…

Q: (f) y = e* In(tanh(x))

A:

Q: dy Find by implicit differentiation. d x e COs x e2y

A: Given query is to find the dy/dx using implicit differentiation.

Q: e* sec (e* +1)dx tanle* +1

A: We need to evaluate ∫ex sec2(ex+1) dxtan(ex+1)                              (1) Let tan(ex+1) = t On…

Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

A:

Q: Q2/ Find by implicit differentiation dx ry3 1+ y* 1+ sec y

A: In implicit differentiation we differentiate without separating the variable

Q: d the derivative of g (x) = Jo cos (t²) dt. COS

A:

Q: y' cos x + y sin x = 1, y(0) = 1. y' = y log, x.

A:

Q: Find dy/dx using logarithmic differentiation a. y=4xx^4

A: Solution is given below:

Q: The rate of heat flow (conduction) between two points on a cylinder heated at one end is given by dQ…

A: Given : rate of heat flow between two points on a cylinder heated at one end is given by…

Q: dy Use logarithmic differentiation to find dr f(z) = (sin(3z))² dy dz

A: The given function is fx=sin3x3x. Determine the differential of the given function. Apply exponent…

Q: x sin x dx = log y dy %3D

A: Let's find.

Q: Using integrating factor, solve dy/dx + 4/x . y = x

A: topic. - differential equations

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.